Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 228 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 8 days (d) 7 days
2. 2.If 2 pens cost ₹30, how much do 8 pens cost? (a) ₹135 (b) ₹240 (c) ₹36 (d) ₹120
3. 3.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 7 days (d) 6 days
4. 4.If 6 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹108 (b) ₹120 (c) ₹75 (d) ₹648
5. 5.If 7 mangoes cost ₹112, how much do 11 mangoes cost? (a) ₹192 (b) ₹116 (c) ₹176 (d) ₹1232
6. 6.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹135 (d) ₹120
7. 7.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹187 (b) ₹34 (c) ₹68 (d) ₹306
8. 8.If 7 mangoes cost ₹133, how much do 10 mangoes cost? (a) ₹1330 (b) ₹209 (c) ₹190 (d) ₹136
9. 9.If 8 kites cost ₹160, how much do 9 kites cost? (a) ₹180 (b) ₹200 (c) ₹1440 (d) ₹161
10. 10.If 6 pens cost ₹66, how much do 10 pens cost? (a) ₹121 (b) ₹70 (c) ₹110 (d) ₹660
11. 11.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹19 (b) ₹54 (c) ₹27 (d) ₹36
12. 12.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹135 (d) ₹81
13. 13.If 4 mangoes cost ₹92, how much do 6 mangoes cost? (a) ₹161 (b) ₹552 (c) ₹138 (d) ₹94
14. 14.If 4 pens cost ₹56, how much do 9 pens cost? (a) ₹504 (b) ₹140 (c) ₹61 (d) ₹126
15. 15.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹245 (d) ₹35
16. 16.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹196 (b) ₹126 (c) ₹56 (d) ₹28
17. 17.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 9 days
18. 18.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 9 days
19. 19.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 9 days (d) 28 days
20. 20.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
21. 21.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹47 (d) ₹423
22. 22.If 7 notebooks cost ₹21, how much do 11 notebooks cost? (a) ₹36 (b) ₹231 (c) ₹33 (d) ₹25
23. 23.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹247 (b) ₹152 (c) ₹38 (d) ₹342
24. 24.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
25. 25.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 33 days (d) 7 days
26. 26.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 3 days
27. 27.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹161 (b) ₹23 (c) ₹138 (d) ₹115
28. 28.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹40 (d) ₹30
29. 29.If 3 kites cost ₹36, how much do 7 kites cost? (a) ₹252 (b) ₹40 (c) ₹96 (d) ₹84
30. 30.If 7 pens cost ₹63, how much do 2 pens cost? (a) ₹58 (b) ₹18 (c) ₹126 (d) ₹27
31. 31.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
32. 32.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 13 days (d) 29 days
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
34. 34.If 8 notebooks cost ₹192, how much do 2 notebooks cost? (a) ₹72 (b) ₹48 (c) ₹384 (d) ₹186
35. 35.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹150 (d) ₹125
36. 36.If 6 pens cost ₹132, how much do 11 pens cost? (a) ₹242 (b) ₹264 (c) ₹1452 (d) ₹137
37. 37.If 2 kites cost ₹48, how much do 9 kites cost? (a) ₹216 (b) ₹55 (c) ₹240 (d) ₹432
38. 38.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹600 (b) ₹101 (c) ₹140 (d) ₹120
39. 39.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹14 (d) ₹49
40. 40.If 3 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹105 (b) ₹23 (c) ₹42 (d) ₹35

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